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What is the Additive Inverse of an Integer?
Grade Level:
Class 6
AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering
Definition
What is it?
The additive inverse of an integer is the number that, when added to the original integer, gives a sum of zero. It's essentially the same number but with the opposite sign. For example, the additive inverse of 5 is -5, because 5 + (-5) = 0.
Simple Example
Quick Example
Imagine your friend gave you Rs. 50. The additive inverse of that is you giving Rs. 50 back to your friend. In terms of money, +50 (receiving) and -50 (giving back) cancel each other out, making the net change zero.
Worked Example
Step-by-Step
Let's find the additive inverse of -12.
1. Identify the given integer: The integer is -12.
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2. Recall the definition: The additive inverse is the number that makes the sum zero when added to the original integer.
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3. Think about the opposite sign: Since the integer is -12, its opposite sign would make it +12.
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4. Check the sum: -12 + (+12) = 0.
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5. Conclusion: The additive inverse of -12 is 12.
Why It Matters
Understanding additive inverses is crucial in many advanced fields like Computer Science and Physics for balancing equations and understanding forces. Engineers use it to design stable structures, ensuring forces cancel out. Even in Data Science, it helps in understanding 'net change' or 'balance' in datasets.
Common Mistakes
MISTAKE: Thinking the additive inverse of a negative number is also negative (e.g., additive inverse of -7 is -7). | CORRECTION: The additive inverse always has the opposite sign. So, the additive inverse of -7 is +7.
MISTAKE: Confusing additive inverse with reciprocal (multiplicative inverse). | CORRECTION: Additive inverse deals with addition to get zero (e.g., 5 and -5). Reciprocal deals with multiplication to get one (e.g., 5 and 1/5).
MISTAKE: Assuming the additive inverse of 0 is undefined or something else. | CORRECTION: The additive inverse of 0 is 0 itself, because 0 + 0 = 0.
Practice Questions
Try It Yourself
QUESTION: What is the additive inverse of 25? | ANSWER: -25
QUESTION: The sum of an integer and its additive inverse is always what number? | ANSWER: 0
QUESTION: If the additive inverse of 'x' is -15, what is the value of 'x'? | ANSWER: 15
MCQ
Quick Quiz
Which of the following pairs are additive inverses of each other?
6 and 1/6
6 and 0
6 and -6
-6 and -6
The Correct Answer Is:
C
Additive inverses are numbers that sum to zero. Only 6 + (-6) equals 0. Options A and B do not sum to zero, and option D shows two identical numbers.
Real World Connection
In the Real World
Think about your mobile data usage. If you use 2 GB of data (+2 GB), and then a friend sends you 2 GB of data back (-2 GB in terms of your usage, or +2 GB for your balance), the net change in your data balance could be seen using additive inverses. Or, in a bank account, a deposit of Rs. 1000 (+1000) and a withdrawal of Rs. 1000 (-1000) cancel each other out, making the net effect zero.
Key Vocabulary
Key Terms
INTEGER: A whole number (not a fraction) that can be positive, negative, or zero. | OPPOSITE SIGN: The same number but with a positive changed to negative, or negative changed to positive. | SUM: The result of adding two or more numbers. | ZERO: The number that represents nothing or the absence of quantity.
What's Next
What to Learn Next
Great job learning about additive inverses! Next, you should explore 'Absolute Value of an Integer'. It builds on understanding positive and negative numbers and will help you measure distance from zero, regardless of direction.
